ANALOG AUTOMATA AND THE FOUNDATIONS OF COGNITIVE SCIENCE

Gert-Jan C. Lokhorst

1991

G.J.C. Lokhorst. Analog automata and the foundations of
cognitive science. In Abstracts of the 9th International
Congress of Logic, Methodology and Philosophy of Science,
Vol. 3, p. 99. Uppsala University, Uppsala, August
1991.

What kind of machines are men? During the past three decades,
cognitive scientists and philosophers of mind have usually worked
on the assumption that we are discrete automata, i.e., entities
which have a countable (usually finite) number of possible internal
states. Thus, men have variously been described as:

Turing machines, i.e., finite automata interacting with an
unbounded discrete environment. This view is to be found in "Turing
machine functionalism" (Putnam 1960) and in most of mathematical
linguistics. (If natural languages are context-sensitive and we do
master them, we are at least linear bounded automata.)

Finite cycle-free transducers (Minsky 1967). Because we are
mortal, such automata are sufficient to account for the whole of a
man's behaviour during his or her lifetime, provided this behaviour
is discrete. Since we have mentioned the four types of automata in
order of strictly decreasing strength, this is the most
conservative assumption one can make.

The supposition that we are discrete automata has recently come
under attack from various circles:

Contemporary "connectionist" models of cognitive and brain
functioning are usually analog, rather than discrete.

Physicists are becoming increasingly fascinated by highly
non-linear, analog dynamical systems; they suggest that we are such
systems ourselves.

Thus, it is becoming more and more plausible that we are analog
automata (having a continuum of possible internal states) rather
than discrete ones.

In this lecture, I will explore the implications the analog
revolution may have for our basic views concerning human cognitive
functioning. I will suggest that it may have less dramatic
consequences than it might appear. On the one hand, there are some
powerful theorems about the possibility of simulating analog
automata by discrete ones. These suggest that both types of
automata are approximately equivalent after all. (Vergis et al.
1986, Rubel 1989). On the other hand, the philosophical theories
which have been stated in terms of discrete automata do not seem to
depend crucially on the notion of discrete states. For example,
Turing machine functionalism may easily be reformulated as analog
automaton functionalism or analog neural network functionalism.

My conclusions are necessarily tentative. The theory of analog
automata is still in an extremely underdeveloped state (less than
half a dozen fundamental articles have appeared since they were
invented by Lord Kelvin), and nobody can tell which surprises the
future has in store.